A new stabilization scenario for Timoshenko systems with thermo-diffusion effects in second spectrum perspective

Abstract

In this work, we analyze a truncated version for the Timoshenko beam model with thermal and mass diffusion effects derived by Aouadi et al. (Z Angew Math Phys 70:117, 2019). In particular, we study some issues related to the second spectrum of frequency according to a procedure due to Elishakoff (in: Advances in mathematical modelling and experimental methods for materials and structures, solid mechanics and its applications, Springer, Berlin, 2010). In Aouadi et al. (2019), the lack of exponential stability for the classical Timoshenko beam with thermodiffusion effects without assuming the nonphysical condition of equal wave speeds has be proved. By using the classical Faedo–Galerkin method combined with the a priori estimates, we prove the existence and uniqueness of a global solution of the truncated version of this problem. Then we prove that this solution is exponentially stable without assuming the condition of equal wave speeds.